Partition function of periodic isoradial dimer models
نویسندگان
چکیده
منابع مشابه
Partition function of periodic isoradial dimer models
Isoradial dimer models were introduced in Kenyon (Invent Math 150(2):409–439, 2002)— they consist of dimer models whose underlying graph satisfies a simple geometric condition, and whose weight function is chosen accordingly. In this paper, we prove a conjecture of (Kenyon in Invent Math 150(2):409–439, 2002), namely that for periodic isoradial dimer models, the growth rate of the toroidal part...
متن کاملThe Dimer Partition Function
We apply the Ginzburg criterion to the dimer problem and we solve the apparent contradiction of a system with mean field α = 12 , the typical value of tricritical systems, and upper critical dimension Dcr = 6. We find that the system has upper critical dimensionDcr = 6 , while for D ≤ 4 it should undergo a first order phase transition. We comment on the latter wrong result examining the approxi...
متن کاملConformal invariance of isoradial dimer models & the case of triangular quadri-tilings
We consider dimer models on graphs which are bipartite, periodic and satisfy a geometric condition called isoradiality, defined in [18]. We show that the scaling limit of the height function of any such dimer model is 1/ √ π times a Gaussian free field. Triangular quadri-tilings were introduced in [6]; they are dimer models on a family of isoradial graphs arising form rhombus tilings. By means ...
متن کاملConformal invariance of dimer heights on isoradial double graphs
An isoradial graph is a planar graph in which each face is inscribable into a circle of common radius. We study the 2-dimensional perfect matchings on a bipartite isoradial graph, obtained from the union of an isoradial graph and its interior dual graph. Using the isoradial graph to approximate a simply-connected domain bounded by a simple closed curve, by letting the mesh size go to zero, we p...
متن کاملComputing a pyramid partition generating function with dimer shuffling
Abstract. We verify a recent conjecture of Kenyon/Szendrői by computing the generating function for pyramid partitions. Pyramid partitions are closely related to Aztec Diamonds; their generating function turns out to be the partition function for the Donaldson–Thomas theory of a non-commutative resolution of the conifold singularity {x1x2 −x3x4 = 0} ⊂ C. The proof does not require algebraic geo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Probability Theory and Related Fields
سال: 2006
ISSN: 0178-8051,1432-2064
DOI: 10.1007/s00440-006-0041-2